Have you noticed that parts a & b are identical?
Do you see a contradiction therein if they were independent?
Suppose that A and B are not trivial events, that is 0< P(A) < 1 and 0 , P(B) < 1. show that
a. if A subset B, then A and B are not independent;
b. if B subset A, then A and B are not independent;
c. if A and B are disjoint then A and B are not independent